John Almon.

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I have submitted to examination, and have found that the reac-
tion taking place may be represented as involving one equivalent
of ohlorid of calcium, one of sulphurous acid, and two of cu-
pric oxyd, and giving rise to one equivalent of sulphate of lime,
and one of dichlorid of copper,

CaCl+SO, +Cu,0, =SCaO, +CuaCI.

A solution of chlorid of calcium holding oxyd of copper in
suspension, rapidly absorbs sulphurous acid gas, and if suffi-
ciently concentrated, is converted into a white crystalline magma
of gypsum and dichlorid of copper. This latter salt I find to
be soluble in a boiling hot solution of chlorid of calcium, which,
however, again deposits it on cooling, a reaction which may
probably be found available on a lar^e scale in separating cop-
per from some other metals. In ordinary cases, nowever, the
precipitation of the dichlorid of copper in the furnace-tank ia
prevented by the presence in the bath of chlorid of sodium, in
which, as is well known, the cuprous chlorid is readily soluble.

The calcined and oxydized ore falling into the tank which
extends sixty feet or more beneath the furnace and its chambers,
is carried forward, with constant agitation, by means of a sub*

Digitized by


308 On the Metallurgical method of Whelpley and Storer,

merged rotating helix, and at length falls into a well at the ex*
tremity, from which it is withdrawn, freed from oxyd of copper,
but generally containing a small residuum of unoxydized sul-
phid, which, if of sufficient importance, is separated by a rejwtition
of the process with the Water-furnace, or oy a rapid calcination
in a reverberatory, of the mass impregnated with chlorids, by
which means the residual copper left by imperfect burning be-
comes readily soluble in the sulphurous chlorid bath of the
water-tank. ,

A small but variable proportion of protochlorid of iron gen-
erally accompanies the chlond of copper, and may be sepAiated
from the cuprous solution by a simple reaction which I also
studied. Three equivalents of cupric oxyd, and two of ferroas
chlorid, yield by their reaction one equivalent each of cuprous
and cupric chlorids, and one of sesquioxyd of iron,


The addition to the heated solution, separated from gypsum
and insoluble matters, of a portion of cupric oxyd therefore suf-
fices to precipitate the whole of the dissolved iron, and the din-
oxyd of copper in the presence of air rapidly produces a simi-
lar result. The addition of milk of lime now throws down,
from the solution of cuprous chlorid, the whole of the copper
as pure hydrous dinoxyd, whose subsequent reduction to the
metallic state is a very simple operation. Meanwhile the chlorid
of calcium is regenerated, and the bath restored to its original
condition may thus be used an indefinite number of times, the
only reagent consumed in the process, in addition to the elements
of the ore, and the oxygen of tne air, being the equivalent of lime
used to precipitate cuprous oxyd.

It will be seen that for sulphuretted ores containing gold, the
treatment in the fire-tower, with the aid of a bath of water only,
affords a simple mode of desulphurization, and leaves the gold
particles in a state most favorable for amalgamation, while in
the case of auriferous ores containing copper, a similar result
may be obtained, and the copper, which is lost in the ordinary
method of working such ores, recovered by means of the chlorid

It is claimed by the designers of this series of processes, that
copper can in this way be produced, at about one-third the cost
of the ordinary method. The small consumption of fuel, and
the mechanical facilities afforded for handling great masses of
material, are such, that the new method will probably be found
especially advantageous, in the treatment of low grade ores, in
regions where transportation is difficult, and fuel scarce. The
patentees have a small experimental furnace eighteen feet high,
at East Boston, but are now erecting at the Harvey Hill mine,

Digitized by


C. Abbe on the Repsold Portable Circle. 809

near Qaebec, a fornace thirty feet high, which, it is expected,
will enable them to treat fifty tons of seven per cent ore in
twenty-foar hours.

The application of the Water-fiirnace to the treatment of the
sulphnretted ores of other metals, presents mai^ points of in-
terest, whose consideration is reserved for another time.

Montreal, Feb. 81, 1867.

Akt- XSXIV.-^ne RepsoU Portable Vertical Circle; by


(CoDtinued from page 216.)

As to the methods and formulas used in connection with the
vertical circle, it is evident that we need first some means of
orientation on arriving at a new station. An observation of any
terrestrial object will give an approximate knowledge of the
zenith pointy and an approximate value of the latitude is easily
had from a map or by estimation. With one pointing upon any
recognizable celestial object, we have then its azimuth and ze*
nith distance for a given observed moment, whence the follow-
ing computation dves us the approximate north point of the
azimuth circle and the hour angle.

Put 90*— ^=a a-^^aziia


[sin a BID j? sin/




The Gaussian formulae give for the azimuth, parallactic angle
and hour angle,


(B.) * Bin a *^ sin I? * siny

tan^A iwaip tan^<=2'.

The computation with its controls is of course performed with
4-figure logarithms. The observed azimuth, plus or minus the
computed A, gives the north point of the circle. The computed
ty plus the tabular R. A., gives the sidereal time, whence is found
the clock correction.

A previously computed ephemeris of the stars to be observed
enables us now to point upon any one. Polaris will naturally
be first chosen, as by it we may more accurately determine the
north point or adjust the azimuth circle to N.P.=0°, as is most
convenient if any number of observations is to be made.
▲m. Joub. Sci.— Skcoud Snnu, Vol. XLIII, No. 129.— Mat, 1867.

Digitized by

Google ~

SIO a Ahbe m the RepsoU Poriabk Circle.

An ephemeria of the azimuths and zenith distances of the
prindpal stais^ if oomputed for every 6° of latitude, will serve
by interpolation for any intermediate position. The formuls
for the compotation of finding ephemerides as given by Mr.
DSllen are ver^ simple.

Pat iK -> (9 — ^)=:r ; the well known fonnola,

0060=006 (7 -«-^) — 20089 006d6in'^<,



(0.) Binir=oo., »inH< ^„(^_j^^y

Another well known formula may be written

/TV\ • A • a <506^

(D.) sm A=sin t t-: 3-7—. .

Or by a transformation of

me eo6A=:— 0069 8in^-|~^°9 eosd cos^i
these results, approximately,

(D'.) 6inaiA=6in 9 m^t -r-^^.

' 8in(9-o)

Neglecting the r in the second members of these equations, they
admit of a very simple arrangement for the computation of a&
ephemeris whose argument is the time for stars near the merid-
ian, being sufficiently accurate within the limits

y-.r>l0*' and <<15^
For an ephemeris in the neighborhood of the prime vertical we
may use the azimuth as argument; counting it from the west
point northward, we have

(K) sin ^=8in 9 co6 2-f-co6 q> sin g Bin A

(F.) tan ^= ein i tan A+tan tpcoit

^ ' 0069

Put tan£= and «=-^ — ;

tan 9 8in 9

the first formula (E) becomes

(G.) co62'=:co8(z— t)=p sin ^ ;

whence ^nrz'iC.

T> » A tanA , co6«

Put tanft»=-: — and w= ;

, 8in9 ' tan^

the second formula (F) becomes

(H.) COB <'=:oo6(r ^m)zxq tan * ;

whence ' <i=:/'±«».

The arrangement of these computations can be made exceeifi
inglv convenient Extensive ephemerides for latitude 35^ to W
iicrai have been published by General Teuner; provided wiA

Digitized by



a Aite anihe Resold Portable Circle. 81 1

diese or similar special ones tbe observer loses no time in select-
iog the pair of stars to be observed. Tbe latitude stars are of
ooorae observed on the meridian as nearly as possible, excepting
tbe polara, which are observed at any hour angle.

In the accurate computation of the results, the following form-
ii]» are used by Mr. DoUen, following Struve's habit of sepa-
titely reducing each observation.

a. For the polars, all observed zenith distances are reduced ta
ihe upper culmination. The formula (C) may be written

(L) «oi(.-C)=co.<.oo.«^*;jj,

IT approximately

(J.) r=ix^iz=z —-__. - ___. sinH'i

sm 1" »ini{«+t)

Provided with the Wrangell or other convenient extended
iUes of sin'^ and assuming an approximate 9 iind zenith
tot and using the value of z+i for the middle of the series
a constant throughout the whole, we easily compote the indi*
lual values of r whence result the circle readings for each ob-
lon as if it had been made at the upper culmination. The
of the four observations circle right and tbe four cirde
gives the correct zenith point, the zenith distance C and the
iximate latitude. With these a second aj^roximation is
, and more will not generally be required. In tbe second
ximation the new refractions and 8ini(2-f C)=8in(<|)— 3+^)
not be anew computed, since the first differences of die
thmic tables will give the Alogr corresponding to the J^9

If the zenith point and latitude are sufficiently well known, it
^ be equally expeditious to compute the direct formula

006C=coa2-|*^co87 coa^ tin^t,
tting of course convenient tables for sin*^^ and Zeeh's tables
for addition.

b. For other stars than the polars observed near the meridian,
the direct computation of logr by means of the following series
till be found convenient We have from (C)

(K.) SID r+28in»^ cot 5=2^^ nn^i ;
^ ' amC


/T\ 1^' ** • ,« ^ • . 9^n «. ^coeyoorf* . ,f

(W ^+^ «><^ { tm 1" - - r « sm* 1", dgc.=:2 .;.,,, am» -.

Regarding the second member as a first approximation to r, and
developing the sin'^t we obtain the following, which is due to

OL) logr=log(|i<»)-^l»;

Digitized by


312 C. Abbe an the Repsold Portflbk Circle.

in which we have pat

p=bourJj gain on sidereal time, /=8eoO+^'

- ^COB9>006^ ^.

^=^ P(J±r)=[9-o223]iKitr).

c. For the compntation of the hour angle from the obeerved
zenith distances in the prime vertical, we have the simple formola

(N.) Ax.m^-^-l—Ai-2-\.

^ ' 2cos9coso\ cost/

cos 2;
the computation of which is sufficiently expeditious even with
six-figure logarithms, if we are provided with the tables pre-
viously mentioned. The second approximation, using a correct
zenith point, is made if necessary as before, by uang the tabu-
lar first differences.

As the formula (A) shows the flexure of the tube to be not
symmetrical with respeet to the zenith, it is necessary for greater
accuracy to correct the results given by each star of a pair, ao
oording to the formula

fzsb mi{z^B).

The correction, f, is directly applicable to the zenith distances
observed for latitude.
For the time determination we have the differential formula

^ ' 16CO89CO6j0 8in/

The application of these corrections is^ especiallv for the lati-
tude, necessary in order to entirely free the result from a pair of
opposite stars from the influence of flexure.

To the preceding sketch of the instrument and its formulas
may be added a few words as to the conduct of the field work,
which may be carried on without inconvenience at a tempera-
ture of 15° or 20° Fahrenheit.

In the Bussian empire, where railroads do not offer sufficient
accommodation to the geodesist, it is necessary that an expedi-
tion should be provided with an easy spring-van drawn by two
or three horses (the Bussian officer is only perfectly happy when
rushing along with his troika). In this covered wagon the
twelve or fifteen chronometers are as well as possible protected
against rapid changes of temperature and disturbing jars. One
or two barometers with thermometers are provided ; the barom-
eters of Brauer's construction have been found to endure aorpris-

Digitized by


C. Abbt on the Repsold Portable Circle. 313

iogly well the rough usage to which they must needs be sub-
jected in journeys of thousands of miles. A heavy tripod is
provided, and the means for leaving a suitable simple mark at
any station* The vertical circle, without being in the least taken
to pieces, is received as a whole into its small neat case in which
two clamps firmly fysten it, an outer thick leather cover with
handles protects the whole, which is carried with ease by two
men, or by one if need be, as it scarcely weighs sixty pounds.
The entire load occupies a space of some twenty cubic feet

Arrived at the previously reconnoitred station, five or ten
oninutes suffice for the two attendants to erect the tripod and set
the vertical circle upon it ; sometimes a block of stone or three
stakes of wood support the feet of the tripod and remain to
mark the station. Meantime the horses havmg been unhitched
and the barometer and thermometers hung up, the chronometers
(including the extremely under- or over-compensated ones) are,
by means of the one beating 18 times in 6 seconds, very rapidly
compared with the one to be used in the observations. The ex-
amination of the state of the instrument and the adjustment of
the verticality of the vertical axis follow, and in a few minutes
after observing the Sun or Moon, Polaris is in the field of view.
Although one determination only of time is necessary, it is bet-
ter to make two, arranging the work as follows :

1. Comparison of chronometer.

2. Reading of barometer and thermometer.
8. Observation of pair of stars for time.

4. Beading of barometer and thermometer.

5. Observation of pair of stars for latitude.

6. Beading of barometer and thermometer.

7. Observation of pair of stars for time.

8. Beading of barometer and thermometer.

9. Comparison of chronometer. '

The observations are now complete and the party may pro*
ceed to the next station ; if any considerable time elapses the
departure should be immediately preceded by another compar-
ison of chronometers.

The time spent at any station must depend upon the skill, en-
ergy and self-devotion of the observer. In the expedition by
DoUen and Hiibner in 1855-56 in the province of Perm, cases
occur where three stations, distant twenty-five to forty miles
from each other, have been thus occupied within the space of
thirty-six hours, the time spent at each being about three hours,
the intervening distances being travelled over very ordinary
roads. It is often very advisable to work expeditiously in order
to improve a few days of consecutive clear weather and secure
a quick return to the starting point, without having exposed
the chronometers to a long absence or dangerous temperature
changes. This latter point is one requiring especial ana intelli-

Digitized by


S14 C. Abbe an the RepsoJd Portable Circle.

gent watchfulness on the part of the observer. Captain Bol-
scheff, having charge of the determination of some two hundred
points in Finnland, mentioned to me the difficulties that he had
to contend with arising from the sudden fall in the atmospheric
temperature during the night, obliging him sometimes to stop
while proceeding from one station to another, not only to make
extra comparisons of his chronometers, but by artificial warmth
to endeavor to counteract the influence of the rapid £ei11 in the
exterior temperature.

Without here farther entering into the details of the methods
pursued by Colonel Smyssloff in obtaining the final corrections
for the rates of his chronometers and the longitudes of his sta-
tions relative to Poulkova, we will note that the twenty stations
here given cover an area of some 135 miles square in the prov-
inces of Novgorod and St Petersburg, and the expeditions occu-
pied him from the 18th of June to the 81st of July, 1859. Two
journeys were undertaken, the first leaving Poulkova June 18th,
visited stations i, 2, ii, 2, ni, 8, 4, 6, 6, i, returning to Poulkova
July 8d. The second left Poulkova July 5th, and visited iv, vi,
7, 8, 9, IV, arriving at Nova Ladoga the 18th of July ; the same
day leaving Nova Lagoda, and visiting 10, iv, 9, 18, V, 14, 15, i,
it returned to Poulkova July 31st. The whole distance travelled
in this six weeks expedition was 1400 miles, of which 175 were
by railroad. Each latitude depends upon eight pointings upon
Polaris and eight upon some southern star ; the probable error
of each resulted in general dbO"'8. Each longitude (as to the
fourteen secondary stations) depends in general upon one time
determination ; the probable error of each is given below. Ten
chronometers were carried, besides the non-compensated one and
the one beating y% seconds and the one used in observing.
There were in all twenty-nine determinations of time and fifteeu
of latitude.

Latitude. I/>nfitade Prob.

Station. Probable error from Poulkova. error.

±0"'8. ±

1. Spasska Orlayno, A 15 68*8 - 6848 0*08

2. Kamenni Polarne, 68 48 898 + 1 28-84 0*07
8. Arm Spasska Poleust, 68 66 16-7 +4 4491 009
4. Koroyay Roastcfaaj, 69 18 24*8 + 8 25-88 0-08

6. Satnoet, 69 29 81*8 4- 8 4620 0-09
8. Uspensko, 69 41 469 + 8 9 00 010

7. Rougoi, 69 28 18 8 +10 761 0*12

8. Oskooa. 69 16 48-5 + 7 2-95 012

9. Podzopie, 69 88 48-6 + 7 1061 010

10. Schaaaenske, 60 8 282 +12 8452 010

11. Taykvayn, 69 88 48-5 +12 44-86 0*08

12. PodflotDO, 69 14 82-2 +12 6278 010
18. Kray^ar Gora, 69 8 81 +11 7-87 0*09

14. Morkonoayzi, 68 60 240 +10 29S8 009

15. Malar Veachera, 68 60 610 + 7 8891 008

16. KoTft Ladoga, 60 6 40-8 +7 68-78 0H>6

Digitized by


C. Abhe an the Repsold Portable Circle. 815

As fundamental points of reference for the longitudes the fol-
lowing list was selected of points determined in previous years.

station. Latituda. LonCitade.

I. PoulkoT^ 69*' 46' 0^ 0^' 0«

IL Louga, 68 48 -0 1 64 *20

III NoTgored, 68 80 -f 8 47 '80

IV. Nova Ladoga, 60 7 -f 7 68 '80

V. BoroTaytache, 68 24 -f 14 19 -98

VL Taykvayn, 69 89 +0 12 44

Of these, however, it was preferred to include iv and vi
among those to be independently determined on the present oo*
casion, and they have received the numbers 16 and 11 in Uie
previous list.

Among several similar expeditions that have come to mv
notice, I may mention those before referred to, of Messrs. Ddl«
len and Hubner in 1856-56 in the government of Perm, where
many points have been unusually carefully determined with
reference to Perm and Ekaterineberg; and that of Captain Bol-
scheff in Finnland in 1863-66, each of whose 160 points has
been twice independently determined.

An extensive series of observations made at Poulkova with
a vertical circle, made in 1857 by Messrs. Bepsold, still farther
attests, if any farther proof were wanted of the reliability of
the results afforded by this instrument — to observe with which
is in fact a luxury of convenience. The observations made on
distant terrestrial signals — the reflection from gilded church
domes — gave for perfect condition of images the probable acci-
dental error of a zenith distance resulting from two pointings
in opposite positions of the circle db0'''62, a large portion of
which may fall upon the level, which was afterwards improved
by the addition of a narrow mirror reflecting the divisions hori-
zontally to the observer's eye.

A suggestion of Mr. DoUen as to the interest that would
attach to a comparison of the results obtained by the vertical
circle with those obtained by using the Talcott zenith telescope
— and the suggestion that by clamping the vertical circle and
observing stars of exactly equal zenith distances, thus freeing
the results from errors ansing from imperfect graduation of the
circle, by converting the vertical circle into a very convenient
zenith telescope — both seem to be well worthy of being put into
execution. In the determination of time I have been able to
apply this latter method of using the vertical circle : it remains
to attempt the same in the determination of latitude.

87 Eaat 20th at, New Taric, January, 1807.

Digitized by


816 E. L. DeForest an Reducing Meteorological Ohservationi.

Abt. XXXV.— On the Reduction of Meteorological Obaervotions;
bj Ebastus L. Deforest.

The sydtem of twelv^e eqaations for oorrecting monthly means
for the unequal length of the months, given by me in this Jour-
naif vol. xlii, page 166, was obtained on the supposition that the
year consists of 366^ days. The true length of the year beine
a very little less than this, it follows that the equations referred
to are not exactly correct The amount of inaccuracy in their
results is indeed very small, but still it seems desirable that fun-
damental formulas of this kind should not involve any unneces-
sary errors, however small they mav be. The equations can be
computed just as well by giving tne year its true length, care
being taken to assign the true values to the arcs n,, n^^n^j and
c, which measure the lengths of the months, ana alBo to the
small arc a;,, which measures the time from the middle of a cal-
endar month to the middle of the corresponding mean month.

On the assumption that the year contains 866*24224 days, a
mean month will contain 80-43686 days, and the calendar month
of February 28*24224 days. A month of 81 days will be rep
resented by the arc 80° 88' 18"-2, a month of 80 days by 29*
84' 9"-9, and the month of February by 27° 60' 12""8. The
values of a, for the several months are therefore








16' 39"-l











4' 6S"-6

31 35 4

51 -3


23 *2



and the twelve equations are found to be

M| =f»i -|-*0037 Wj +'0030 m^a— '0067 m.
Ma =ma — '0127 m^

M, =»l3 +-0028 lllg

M. =i»^ -•0042 111^ ^•0200 111


+•0016 m^
— -0039 fill,

—•0031 m,
^•0249 m^

—•0218 m^
-•0180 m,

- •0168 iWj
+•0221 m^
- -0242 m^
+•0202 me
+•0219 mj
- •0174 m.


+•0026 mj —-0200 m^
-f-0025 mg —-0103 m^ +-0078 m^
-•0027 mg — •0067m3 +0094 m,,,
M,^=:mi^+0030 mio-'0085 m^ +^0056 m^ ,
Mji=mjj— -0026 m„— -0046 m,^+'0072 m^^
Mia=mja+0032 mja-^0064 m^j+'0032 m^

It will be seen that the numerical coefficients here given differ
from the previous ones to the amount, in some cases, of a single
unit in the fourth decimal place. They are, I believe, as nearly
exact as they can be made without extending them beyond the

Digitized by


E> L. DeForeit on Reducing Meteorological Observations, 817

fourth place, a degree of refinement which would be practicallj
useless. The computation, however, was carefully made to six
places, so as to secure the nearest value for the last figure. In
rejecting the fifth and sixth places, care has been taken not to
impair the condition that in any single equation the sum of the
thiee decimal coefficients must be zero. The first and seventh
equations, as computed to six places, are

Mj=m^+-003668 mi+-003060 mj^— "006728 m^
^ M7=m7-i-'002541 my-'OlQQSl m^ +017440 m^.

When these are reduced to four places in the usual way, they


M,=mj+-0037 mj+-0031 mj^— '0067 m^
U^=im^+'0025 m^ -.-0200 f»g +-0174 m^.

The sums of the three decimal coefficients differ firom zero to
the amount of a single unit in the fourth place ; and to correct
this, the unit has been added to or subtracted from that coeffi-
cient which is least altered by it, as compared with its true value
to six places.

Since the length of a calendar year is either 865 or 866 days,
the assumption that the year consists of 865*24224 days is not
strictly applicable to meteorological observations for any singfe
year. But the average length of a considerable number of con-
secutive calendar years approaches very closely to that of the
true or astronomical year, and the greater the number of years
the closer will be the approximation. Therefore when we are
considering the mean results of observations which have ex-
tended over a long course of years, the assumption that calendar
years and astronomical years are equal will lead to no error.
In the same way we are justified in assigning 28*24224 davs to
February, because this is the average length of that month for
a series of many consecutive years.

When the equation of the curve representing the annual
course of any meteorological phenomenon, as the mean daily

Online LibraryJohn AlmonThe American journal of science and arts → online text (page 37 of 102)